How to recognize non-circular radial symmetry in images?
The Hough Transform extended to orthogonal ellipses uses this model, accumulating on $\theta$ for all $\{x, y\}$ with parameter matrix

\begin{Bmatrix} 
c_x &amp; c_y \\ 
r_x &amp; r_y
\end{Bmatrix}

where

$$1 = \dfrac {(x - c_x) \, \cos \theta} {r_x} + \dfrac {(y - c_y) \, \sin \theta} {r_y}$$

The question is looking to detect the normal lines, so any of the several algorithms for the above model can be modified to accumulate on $r$ for all $\{x, y\}$ with parameter matrix

\begin{Bmatrix} 
c_x &amp; c_y  \\ 
r_x &amp; r_y
\end{Bmatrix}

where

$$0 = \dfrac {x - c_x} {r_x} + \dfrac {y - c_y} {r_y}$$

Lines that intersect $(c_x, c_y)$ don't rely on $r_x$ or $r_y$.  However, it may be useful to recognize that, if radially equally spaced, viewing the lines from a position other than one that projects into the plane of the lines at $(c_x, c_y)$ will present a line density that is a function of $\arctan (r_x, r_y)$.